References
- Han D, Dai H, Qi L. Conditions for strong ellipticity of anisotropic elastic materials. J Elasticity. 2009;97(1):1–13.
- Qi L, Hu S, Zhang X. Biquadratic tensors, biquadratic decomposition and norms of biquadratic tensors. preprint, arXiv: 1909.13451.
- Wang X, Che M, Wei Y. Best rank-one approximation of fourth-order partially symmetric tensors by neural network. Numer Math Theor Meth Appl. 2018;11(4):673–700.
- Stavrou SG. Canonical forms of order-k (k = 2, 3, 4) symmetric tensors of format 3 × · · · × 3 over prime fields. Linear Multilinear A. 2015;63(6):1111–1124.
- Zou W, He Q, Huang M, et al. Eshelby's problem of non-elliptical inclusions. J Mech Phys Solids. 2010;58(3):346–372.
- Dahl G, Leinaas JM, Myrheim J, et al. A tensor product matrix approximation problem in quantum physics. Linear Algebra Appl. 2007;420(2–3):711–725.
- Chiriţă S, Danescu A, Ciarletta M. On the strong ellipticity of the anisotropic linearly elastic materials. J Elasticity. 2007;87(1):1–27.
- Doherty AC, Parrilo PA, Spedalieri FM. Distinguishing separable and entangled states. Phys Rev Lett. 2002. Available from: https://doi.org/10.1103/PhysRevLett.88.187904.
- Gurvits L. Classical deterministic complexity of Edmonds' Problem and quantum entanglement. In: Proceedings of the Thirty-Fifth ACM Symposium on Theory of Computing. ACM: New York; 2003. p. 10–19.
- Ling C, Nie J, Qi L, et al. Biquadratic optimization over unit spheres and semidefinite programming relaxations. SIAM J Optim. 2010;20(3):1286–1310.
- Qi L, Chen H, Chen Y. Tensor eigenvalues and their applications. Singapore: Springer; 2018.
- Qi L, Dai H, Han D. Conditions for strong ellipticity and M-eigenvalues. Front Math China. 2009;4(2):349–364.
- Wang Y, Qi L, Zhang X. A practical method for computing the largest M-eigenvalue of a fourth-order partially symmetric tensor. Numer Linear Algebr Appl. 2009;16(7):589–601.
- Li S, Li C, Li Y. M-eigenvalue inclusion intervals for a fourth-order partially symmetric tensor. J Comput Appl Math. 2019;356:391–401.
- Zubov L, Rudev A. A criterion for the strong ellipticity of the equilibrium equations of an isotropic non-linearly elastic material. J Appl Math Mech. 2011;75(4):432–446.
- Ding W, Liu J, Qi L, et al. Elasticity M-tensors and the strong ellipticity condition. Appl Math Comput. 2020. Available from: https://doi.org/10.1016/j.amc.2019.124982.
- Huang Z, Qi L. Positive definiteness of paired symmetric tensors and elasticity tensors. J Comput Appl Math. 2018;338:22–43.
- He J, Li C, Wei Y. M-eigenvalue intervals and checkable sufficient conditions for the strong ellipticity. Appl Math Lett. 2019. Available from: https://doi.org/10.1016/j.aml.2019.106137.
- Li S, Li Y. Checkable criteria for the M-positive definiteness of fourth-order partially symmetric tensors. B Iran Math Soc. 2019;46:1455–1463.
- Sfyris D. Comparing the condition of strong ellipticity and the solvability for a purely elastic problem and the corresponding dislocated problem. Math Mech Solids. 2012;17(3):254–265.
- Gloub GH, Van Loan CF. Matrix computations. 3rd ed. Baltimore (MD): Johns Hopkins Universtiy Press; 1996.
- Bakri Z, Zaoui A. Structural and mechanical properties of dolomite rock under high pressure conditions: a first-principles study. Phys Status Solidi B. 2011;248(8):1894–1900.